With a bold outlay of $7.5 billion, the Abu Dhabi Investment Authority is about to become one of the largest shareholders in Citigroup.

The bank had already experienced the petrodollar’s power this month when another major shareholder, Prince Walid bin Talal of Saudi Arabia, cleared the way for the ouster of its chief executive, Charles O. Prince III.

The Dubai stock exchange, meanwhile, is negotiating for 20 percent of a newly merged company that includes Nasdaq and the operator of stock markets in the Nordic region. Qatar, like Dubai a sheikdom in the Persian Gulf, might compete in that deal..

In late October, Dubai, which has little oil but is part of the region’s energy economy, bought part of Och-Ziff Capital Management, a hedge fund in New York. Abu Dhabi this month invested in Advanced Micro Devices, the chip maker, and in September bought into the Carlyle Group, a private equity giant.

Experts estimate that oil-rich nations have a $4 trillion cache of petrodollar investments around the world. And with oil prices likely to remain in the stratosphere, that number could increase rapidly.

In 2000, OPEC countries earned $243 billion from oil exports, according to Cambridge Energy Research Associates. For all of 2007 the estimate was more than $688 billion, but that did not include the last two months of price spikes.

“If you look at gulf countries, they have a total common economy that is about the size of the Netherlands,” said Edward L. Morse, chief energy economist of Lehman Brothers. “These are tiny countries, but they have to place collectively over $5 billion a week from their oil revenues. It’s not an easy thing to do.”

The explosion in investment has set up some of its own cross-currents. While the recent decline in the value of the dollar is making investment in the United States cheaper, many investors are holding back out of fear that the dollar will decline further, diminishing the worth of their dollar holdings.

Many oil investors are also worried about a potential political reaction in the United States similar to the furor of last year when Dubai tried to acquire a company that operates American ports. European leaders, at the same time, worry that Russia is using its oil revenues to snatch up pipelines and other energy infrastructure in their region.

Such concerns seem to be driving investments to other parts of the world, many analysts say.

“The investments are diversifying outside the United States, though the U.S. still has the bulk of it,” said Diana Farrell, director of the McKinsey Global Institute, a research arm of the McKinsey consulting firm, which calculated in October that petrodollar investments reached $3.4 trillion to $3.8 trillion at the end of 2006.

“Europe is a prime target,” she added, “but at least 25 percent of foreign investments from the Persian Gulf are in Asia, the Middle East and North Africa.”

Though oil-producing countries have been looking at investments in the West since the 1970s, their strategies back then were largely confined to safe assets with a low return, like United States Treasury debt.

By 2001, with the collapse in oil prices, many of the oil exporters had depleted their dollar reserves, economists say.

But the boom in oil prices in the last five years has changed all that. It has persuaded oil producers to set up or expand “sovereign wealth funds” as vehicles to invest far more aggressively in the West, in their own economies and in emerging markets.

Other petrodollar investments are made through government-owned corporations, corporations and individuals like Prince Walid, who owns stakes not only in Citigroup but also News Corporation, Procter & Gamble, Hewlett-Packard, PepsiCo, Time Warner and Walt Disney.

The oil-rich nations are also investing more in real estate, private equity funds and hedge funds, analysts say, and increasingly they are investing the money on their own, bypassing the major financial institutions of the United States and Europe.

“The oil-producing countries simply cannot absorb the amount of wealth they are generating,” said J. Robinson West, chairman of PFC Energy. “We are seeing a transfer of wealth of historic dimensions. It is not just Qatar and Abu Dhabi. Investment funds are being set up in places like Kazakhstan and Equatorial Guinea.”

Precise figures of the global picture in petrodollars are not easy to come by, in part because the big investors in the Persian Gulf and elsewhere are not obliged to disclose their portfolios or activities.

The lack of transparency is a problem to leaders of Western industrial economies. In October, Henry M. Paulson Jr., Treasury secretary of the United States, and the finance ministers of other major industrial democracies called for an international code of “best practices” by cross-border investors requiring greater disclosure of assets and actions.

The petrodollar era has benefited the world economy, economists say, notably by enhancing liquidity at a time when foreign currency reserves of export giants in Asia are also making the world flush with cash.

Recently Ben S. Bernanke, chairman of the Federal Reserve, has spoken of a “global savings glut” that has lowered interest rates worldwide. Ms. Farrell, of the McKinsey Institute, estimates that petrodollars may have kept American interest rates three-quarters of a percentage point lower than they would otherwise be, a direct benefit to American consumers.

But the flood of investments is also causing problems, like overheated economies and asset bubbles in oil-rich nations.

“The gulf countries are pouring credit into their economies, adding to excess liquidity,” said Charles H. Dallara, managing director of the International Institute of Finance, an organization of leading private financial companies. “It is eroding the earning power of local citizens and becoming a source of economic instability over time.”

Some investment deals have fallen through, to the embarrassment of all sides. This year Qatar sought to do a leveraged buyout of a retailer in Britain, the J Sainsbury supermarket chain.

After starting the bid in July, Qatar faced concerns from unions, the Sainsbury family and others over whether the Qataris wanted Britain’s third-largest grocery chain just for the underlying real estate and whether the company could survive the amount of debt being incurred. The deal fell through three weeks ago, , when Qatar said that the global credit squeeze made the borrowing costs too high.

The decline in the dollar has also introduced new uncertainties into predicting petrodollar investment patterns. C. Fred Bergsten, director of the Peterson Institute of International Economics, said that while some countries in the gulf were trying to diversify their investments away from the dollar and into euros and pounds sterling, the Saudis were trying to quell that trend out of fear that the dollar will decline further and diminishing the value of their assets.

A measure of discord over the dollar was apparent at the OPEC meeting in Saudi Arabia this month. Iran and Venezuela, the two biggest political foes of the United States among the oil producers, complained that oil was being sold in a currency whose value was eroding by the day.

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